How to treat negative integer factorial function?

[dongsh2]

Dear all,

How to deal with negative integer factorial functions? I mean what expression formula can be substituted for this?

 

[Vanadium 50]

I don't believe there is one. The Gamma function is the analytic continuation, but it has poles at the negative integers.

 

[HallsofIvy]

The first thing you would have to do is define this "negative factorial function". Where did you find a reference to a "negative factorial function"? If this was given in some text exercise how was the negative factorial function defined?